Question

A biconvex lens made of glass of refractive index 1.5 has radius of currature of both of its surfaces as 40cm. Calculate the (i) power and (i) focal length ofthe lens. Also find out the change in the focal length of the lens when it is submerged in water. (The refractive index of water with respect to air, n = 1.33)​

Answer 1

Answer:

hence, focal length changes 18 to 32

Answer 2

(I). The power of the lens is 2.5 D

The focal length of the lens is 40 cm

(II). The change in the focal length of the lens is 116.47 cm.

Explanation:

Given that,

Refractive index = 1.5

Radius of curvature of R ₁ of first convex lens= 40 cm

Radius of curvature of R₂ first convex lens= -40 cm

We need to calculate the focal length of the lens

Using formula of focal length

$\dfrac{1}{f}=(\mu-1)(\dfrac{1}{R_{1}-\dfrac{1}{R_{2}}})$ ...(I)

Put the value into the formula

$\dfrac{1}{f}=(1.5-1)\times(\dfrac{1}{40}-\dfrac{1}{-40})$

$\dfrac{1}{f}=\dfrac{1}{40}$

$f=40\ cm$

(I). We need to calculate the power

Using formula of power

$P=\dfrac{1}{f}$

$P=\dfrac{100}{40}$

$P=2.5\ D$

The power of the lens is 2.5 D

The focal length of the lens is 40 cm

(II). When it is submerged in water

We need to calculate the focal length

Using formula of focal length

$\dfrac{1}{f}=(\dfrac{\mu_{g}}{\mu_{w}}-1)(\dfrac{1}{R_{1}}-\dfrac{1}{R_{2}})$

Here,$(\dfrac{1}{R_{1}}-\dfrac{1}{R_{2}})=A$

$\dfrac{1}{f_{1}}=(\dfrac{\mu_{g}}{\mu_{w}}-1)A$...(II)

Now from equation (I)

$\dfrac{1}{f}=(\mu-1)A$

$\dfrac{1}{40}=(1.5-1)A$....(III)

Now, from equation (II)

$\dfrac{1}{f_{1}}=(\dfrac{1.5}{1.33}-1)A$...(IV)

Divided equation (III) by equation (IV)

$f_{1}=\dfrac{40\times(1.5-1)}{\dfrac{1.5}{1.3}-1}$

$f_{1}=156.47\ cm$

We need to calculate the change in focal length

Using formula of focal length

$\text{change in focal length}=f_{1}-f$

$\text{change in focal length}=156.47-40$

$\text{change in focal length}=116.47\ cm$

Hence, (I). The power of the lens is 2.5 D

The focal length of the lens is 40 cm

(II). The change in the focal length of the lens is 116.47 cm.

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Topic : focal length

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